This chapter constructs exact non-Gaussian preparation states from the one-dimensional Schrödinger equation. The construction is algebraic: a ...
This chapter develops a two-dimensional charged oscillator from the basic minimal-coupling rule. No prior magnetic-oscillator calculation is a...
A charged harmonic oscillator in an external magnetic field appears to be a simple quantum-mechanical system, yet it provides a clean setting ...
Shape invariance is one of the central algebraic mechanisms behind exactly solvable quantum potentials in supersymmetric quantum mechanics. In...
Angular momentum in quantum mechanics is not merely the quantization of $\mathbf{L}=\mathbf{r}\times\mathbf{p}$. That formula describes one sp...
We study a two-degree-of-freedom model with a velocity-coupling term and an inverse-square interaction. The classical dynamics becomes transpa...
Advanced concepts in Lagrangian mechanics, including generalized coordinates, nonstandard Lagrangians, and coupled systems.
Exact Solution on Shifted Contour Starting from the radial Schrödinger equation on the complex-shifted contour $r=x-i\varepsilon,; x\in(-\inft...
A defining insight of modern theoretical physics is that the fundamental laws of nature are governed not merely by differential equations, but...
Why Study Lie Superalgebras in Supersymmetry
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